tl;dr: use the following from a console:

$ sudo apt install -t jessie-backports openjdk-8-jre-headless ca-certificates-java

JOSM needs Java-8. Open-Java-8 is available via Jessie Backports, but the current update (8u121-b13-1~bpo8+1) needs updated CA-Certificates which were not previously available from Backports (see Debian bug#851667). Unfortunately, Synaptic will not spot the updated certificates in Backports since it keeps holding back openjdk-8-jre, etc.. Thus, the need to use the console line as at top.

Unfortunately, I’d worked my way through the very-useful AskUbuntu question on:

“E: Unable to correct problems, you have held broken packages”

…and had therefore removed all Oracle + OpenJDK Java8 (which meant that all JOSM was also gone & all my Java alternatives reverted to Java7). However, it also meant that I had a different error message on attempted reinstall of Java-8:

$ sudo apt-get install openjdk-8-jre openjdk-8-jre-headless ca-certificates-java
  ...
  The following packages have unmet dependencies:
   openjdk-8-jre-headless : Breaks: ca-certificates-java (< 20160321~) but 20140324 is to be installed
  E: Unable to correct problems, you have held broken packages.

That allowed me to find a Unix Stack Exchange Q which solved the issue. Now I need to reinstall JOSM & make Java-8 the system default (sigh)…